On Games, Meta Games, and the Infinite Game

Our core values are, in no particular order: Challenge; Authenticity; Care; Responsibility. We came to these values over a long time and a lot of thought and rigour. They are not simply preferences of ours. They are discovered, not invented. For us these are primary values, from which all other values emerge. Even our algorithm is constructed based upon these values, as algorithms are never value-neutral.

This is where these values come from.

A goal is an intent to generate an imagined reality.

A pursuit is a recurring goal or set of goals.

A purpose is a series of pursuits and goals.

To be an agent is to have purposes.

To create is to fulfill a goal.

An environment is a set of constraints and enablers that a pursuit interacts with.

A space is an environment created for a particular pursuit, such as a football pitch, or a web forum, or a house.

A good pursuit is one whose goal, or goals, correlate with the agent’s purpose.

  • When goals and pursuits correlate with their purpose it means the subsequent goals become easier to achieve, or are directly achieved.
  • Goals can have multiple purposes.

The meaning of a pursuit is the description of the relationship between the goals and the purpose, in other words why they correlate. So the meaning of a pursuit is the reason an agent engages in the pursuit.

A pursuit that becomes trivial is called a fixed action pattern, and no longer requires an agent.

  • Fixed Action Pattern is a term used in ethology to describe unconscious actions and reactions to stimuli in animals and plants.

Optimisation for a pursuit increases agency for the purpose by reducing agency for the parts

  • E.g. A tennis player may practice and visualise a particular type of swing until it is almost automatic, converting conscious intent into a fixed action pattern

A strategy is a set of fixed action patterns that can be deployed to achieve a goal or set of goals. A strategy is optimised as it expands the set of fixed action patterns to respond to a wider variety of scenarios in the possibility space.

Tactics are the specific fixed action patterns deployed in a game.

A competition is a pursuit in which the success of agents is determined relative to each other.

A goal of one agent may serve the purposes of another. We call this positive-sum.

If the goal of one agent contradicts that of another, then the total sum of the energy input by each player can equal or exceed the total sum of the value output. We call this zero-sum or negative-sum. If one agent concedes before this point then the pursuit remains positive sum.

The goals of multiple agents may be independent, in conflict, in alignment, or in confluence. The purposes of multiple agents can be, at different times, independent, in conflict, in alignment or in confluence.

Independence is where there is no intersection of goals.

A conflict is a contradiction of purposes, which is always negative sum, as agents inhibit each other’s goals in order to advance their own purposes.

Alignment is the state of agents having common goals.

Confluence is the state of agents having common purposes.

A game is a pursuit engaged by agents without regard to the correlation between the goal and its purpose, as in a goal pursued for its own sake. In other words, to ‘game the system’ is to pursue the goal at the expense of the sustainability or robustness of the system.

An agent in a game is a player.

A good game is one which remains robust regardless of the strategies deployed by players. (Nash Equilibria).

Since an agent can have multiple purposes, but can only attend to one goal at a time, a player may go in and out of a game repeatedly, by redirecting their attention.

If a goal serves the purposes of an agent outside the game we say that the agent is interested in the game.

Games can be used by agents to select between players when success within the game correlates with success in that agent’s purposes.

Selection by interested agents may also serve the purposes of players.

A player that aims to be selected by an external agent is in service of that agent. Thus we say that a player’s purposes can be in service of a set of selecting agents.

There may be multiple selecting agents, in which case a game emerges between selectors, to win the service of players. This two-way selection process changes both categories of agents over time as they optimise for the objective function of the other, and is called dimorphic selection.

  • Dimorphic selection is the term given to the morphological differences between males and females due to different selection pressures acting on each category. Humans are less dimorphic than other species, like gorillas or black widow spiders. But dimorphic selection applies to any two-way selection process that changes each category, e.g. consumers and products, employers and employees, predators and prey, or an arms race, where the relationship between agents is punctuated by conflict rather than confluence.

The games used on both sides to be selected are called proxy games, because they correlate with and represent the agents’ capacity to engage in further games that serve their purposes.

For a proxy game to be interesting to selecting agents it must be difficult* and verifiable*.

  • If the goal of a game is not difficult it is trivial, increasing the cost to distinguish between the success of players for the selecting agents, which decreases its efficiency.
    • A trivial game may be a necessary proxy game for a less trivial and more meaningful game, and thus becomes a fixed action pattern. Agency is not required to implement a fixed action pattern, and thus the game loses its agent.
  • If the goal of a game is not verifiable the meaning is unknown, and thus the game loses its purpose.

Furthermore, for a game to be a useful selection proxy it must be inclusive* and independent*.

  • If the game is not inclusive it means it is excluding potential players for reasons unrelated to the goals of the game and the purposes of the selectors, and thus players and selectors will choose a different, more universal game if it is available.
  • If the game is not independent it means success is partially or wholly determined or influenced by a third-party agent, who can have their own implicit purposes which may or may not be in confluence or alignment with the purposes of players and selectors.
    • Another way of describing independence is the orthogonality of the verification mechanism. In Bitcoin, the nodes that verify the result of the proof of work algorithm are a set of independent third parties which may have their own interests, but it is their orthogonality which makes the system work, because they cannot coordinate.

The extent that games fulfill these constraints – difficulty, verifiability, inclusivity and independence – is the extent that they are stable, retain their meaning, meaning robust against entropy.

A crisis of meaning happens when the games used by agents to fulfill their purposes lose their meaning.

We call these constraints meta rules because both players and game designers can contribute to preventing a crisis of meaning, to reducing disorder and chaos, to the extent that they act within these constraints, as a generalisation of the explicit constraints of the game itself.

When a player uses a game for the purposes of being selected we call this a selection signal.

A player may imitate success, what we call cheating, in order to be selected. These false signals, we call noise.

The robustness of a game system is measured by the signal to noise ratio output by its composite proxy games.

Signal is a form of information.

Entropy is a measure of the rate of change in the amount of energy required to describe or model a system at any time ‘t’.

Since entropy is a measure of information in a system, the amount of noise directly correlates with the rate of entropy, or the tendency towards disorder. In other words, as noise increases it increases the cost of describing or modelling the state of the game.

Therefore an agent does not contribute to the entropy of a game system when they work hard and sacrifice (difficulty), don’t lie or cheat (verifiability), do not exclude anyone for reasons unrelated to the goals of the game (inclusivity), and take responsibility (independence).

A game designer generates negentropy when they generate the rules and constraints of the game system that produce more signal and less noise, in other words that the goals are difficult, verifiable, inclusive and independent.

Rules are descriptions of constraints that prevent entropic strategies being employed in a game, which authorise some agents to prevent the use of these strategies with force, called a sanction.

Good rules are a set of explicit or understood regulations or principles constraining the conduct or procedure within a game which are in accordance with the meta rules.

Bad rules are a set of explicit or understood regulations or principles constraining the conduct or procedure within a game which are in discordance with the meta rules.

In mature games optimal strategies emerge which also constrain players, but even though these strategies can be formalised, they are not rules. Such are the dominance of optimal strategies though, that they may be experienced as having the same force as a sanction for deviating from a rule, and can therefore be called nominal rules – rules in name only. Indeed, in less formalised games it can be difficult to distinguish between real rules and nominal rules.

The meta player is the player who challenges or inspects the rules critically, to discover new strategies that disrupt existing hegemonies by distinguishing real rules from nominal rules, including employing strategies to change the rules, and thus change the game.

A player who challenges the meta rules leaves the game and increases entropy.

Governance is the process of setting the rules by which a set of games are played.

A meta game is the game of governing a specific game.

Good governance is the process of setting the rules by which a game is played such that the game retains its order, meaning it is meta stable.

Bad governance is the process of setting the rules by which a game is played such that the game tends towards disorder, or meta chaos.

The game of governance across the set of all possible games is called the infinite game, or the game of creating or designing games.

Games mediate the relationships between agents, allowing them to achieve goals more efficiently, without having to attend to the goals and broader purposes simultaneously.

Where goals are in conflict, but purposes are in alignment, a mechanism emerges to resolve the conflict such that both parties continue in their purpose as efficiently as possible. This is called a rivalrous game, and it determines whose goal takes priority. For example, a queue in a supermarket, a sport, exams, or democracy.

Like any other game, a rivalrous game can be good or bad. Rivalry itself is not the cause of self-termination. Rivalry is a mechanism for continuing a game even when players are in conflict, and the value of that mechanism is determined by its correspondence to the meta rules.

Society is the aggregate of all of the selection games used to bring players into confluence.

A good society is meta stable, as in has a low rate of entropy.

A bad society is meta chaotic, as in has a high rate of entropy.

Community is the state of players being in confluence.

Good governance is a prerequisite for a good society, and a good society is a prerequisite for nurturing and growing communities, therefore good governance is a prerequisite for growing communities.

Therefore, good governance means setting the rules so that they foster challenge (difficulty), authenticity (verifiability), care (inclusivity), and responsibility (independence).